The combination flow is great and I love family names! I will admit that when I hear Parks I immediately think......and recreations.

This, completely.

If I heard it on the playground, I'd honestly think I misheard it. Some word names sound like they could be names (River, Olive, Sage) and some, like this one, do not. This is obviously just one stranger's opinion though!

Honestly, I think I would prefer just Park. Parks feels plural and too word-like. Like naming someone Gyms.
I like Park alright because it's similar to Mark or Lark. It maintains the spirit without being an entirely different name, but is easier to swallow for me.